US 7720661 B2 Abstract A method for a geometry of a lateral comb drive for an in-plane, electrostatic force feedback, closed-loop, micromachined accelerometer or closed-loop Coriolis rate gyroscope device, or closed-loop capacitive pressure or force measuring device. When vibration is applied to the device, the error in the time-average output, which is vibration rectification error, due to this input vibration is minimized or eliminated. The geometry resulting from practice of the present invention is space-efficient because drive force is maximized while vibration rectification is minimized or eliminated.
Claims(13) 1. A method for making a microelectromechanical system (MEMS) electrostatic comb-drive device, the method comprising:
constructing a finite element model of an initial comb tooth geometric unit;
selecting an initial comb tooth overlap dimension;
performing a finite element analysis calculation of capacitance for both the selected initial overlap dimension and for each of one or more different overlap dimensions adjacent to the initial overlap dimension;
constructing a model of a relationship of capacitance versus overlap dimension;
applying a second derivative test to solve for an inflection point in the relationship of capacitance versus overlap dimension;
selecting an overlap dimension corresponding to the inflection point; and
making a MEMS electrostatic comb-drive by orienting a movable proof mass having comb teeth to a stationary comb tooth frame, so that the comb teeth and the stationary comb tooth frame overlap by the selected overlap dimension.
2. The method of
3. The method of
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9. The method of
initially adjusting a position of the proof mass relative to the frame to a position of non-zero differential capacitance;
vibrating the adjusted proof mass relative to the frame along an input axis;
additionally adjusting the position of the vibrating proof mass relative to the frame to a position where fluid forces operating on the proof mass are balanced relative to the comb tooth geometry, thereby calibrating the MEMS device.
10. The method of
11. The method of
vibrating the device along an input axis; and
balancing fluid forces operating on the vibrating proof mass with the actual comb tooth geometry.
12. The method of
13. The method of
wherein adjusting a position of the proof mass relative to the frame to a different relative position where fluid forces operating on the proof mass are balanced with the actual comb tooth geometry further comprises, after initially adjusting the relative position of the proof mass to the zero rectification position and during vibrating the device, additionally adjusting the position of the proof mass relative to the frame.
Description The present invention relates to micromachined sensor devices and methods, and in particular to electrostatic comb-drive, closed-loop, in-plane, micromachined, capacitive accelerometers, Coriolis rate gyroscopes, and pressure and force measuring devices. Microelectromechanical system (MEMS) capacitive electrostatic comb-drive, closed-loop, in-plane, micromachined, capacitive pick-off accelerometer devices, closed-loop Coriolis rate gyroscope devices, and closed-loop capacitive pressure and force measuring devices are generally well-known. In particular, silicon-based, micromachined accelerometers are displacing accelerometers of more mature architectures in current applications, and are creating new markets where the advantages of small size and low cost are enabling qualities. One critical area of performance that poses a major challenge for MEMS capacitive accelerometers is vibration rectification. Vibration rectification is the change in the time-average accelerometer output due to input vibration. Vibration rectification manifests as an apparent change in the DC acceleration when none is being experienced. Current MEMS capacitive accelerometers, Coriolis rate gyroscope devices, and closed-loop capacitive force measuring devices have very poor vibration rectification performance. For example, an input vibration of 10 Grms along the input axis of a known electrostatic comb-drive MEMS capacitive pick-off accelerometer is able to change the average output by as much as 0.1 g's. This large vibration rectification makes these accelerometers unsuitable for current tactical and navigation-grade applications. In a closed-loop capacitive pick-off accelerometer, rectification error is driven by several sources. For example, rebalance force is not linear relative to the voltage applied to the electrostatic comb-drive. The rebalancing force is proportional to the square of the applied voltage difference between sets of interacting moveable and fixed comb teeth. There are several well-known ways to accomplish linearization of the applied voltage. For example, a square root function can be placed in the feedback loop. The various methods of linearizing this relationship, however, are not relevant to the present invention. Scale factor may have asymmetry in a closed-loop capacitive pick-off accelerometer. That is, the scale factor in the positive input direction may not equal the scale factor in the negative direction. The scale factors in the two directions must match to avoid rectification. This is also well-known, can be corrected for, but is not relevant to the present invention. A third source of rectification in a closed-loop capacitive pick-off accelerometer is a dependence of rebalance force on proof mass position. In current art, closed-loop MEMS capacitive pick-off accelerometers with electrostatic feedback use one of two configuration options. A fourth source of rectification is a force that a damping fluid exerts on the proof mass during vibration. Typically, MEMS accelerometers rely on gas damping to achieve acceptable dynamic performance. Gas-spring damping effects, however, often produce a non-zero time average force on the proof mass as it travels through a cycle of vibration. Many variables affect this rectification error which is a function of the detailed geometry of the damping gaps, the gas type, pressure and temperature, and the magnitude and frequency of the input vibration. The result is a highly complex fluid dynamics problem. Furthermore, the magnitude of this rectification error is potentially extremely large. Therefore, devices and methods for overcoming these and other limitations of typical state of the art MEMS accelerometers are desirable. The prior art fails to provide a method for determining a lateral comb drive geometry which minimizes or completely eliminates rectification and, at the same time, provides a sufficiently large force for a given drive area and applied voltage. What is needed in the art is a method for significantly reducing or eliminating this source of rectification within a compact drive geometry. The method of the present invention provides a geometry of a lateral comb drive for an in-plane, electrostatic force feedback, micromachined accelerometer, closed-loop Coriolis rate gyroscope devices, and closed-loop capacitive pressure and force measuring devices. When vibration is applied along an accelerometer's input axis, the error in the time-average output, which is the vibration rectification error, due to this input vibration is minimized or eliminated. The geometry resulting from practice of the present invention is space-efficient because drive force is maximized while vibration rectification is minimized or eliminated. The present invention is an apparatus and method for reducing rectification error in a microelectromechanical system (MEMS) electrostatic comb-drive, closed-loop, in-plane, accelerometer device. This invention provides both an analytical and empirical method of locating a comb tooth overlap that results in minimum or zero rectification error for any chosen general tooth geometry. The method includes: selecting an initial comb tooth geometry, including selecting initial tooth width and length dimensions, and the spacing between each moveable tooth and the adjacent fixed tooth. These selections are made as a function of overall design requirements and silicon fabrication design rules. A finite element model is constructed of at least one tooth pitch of the initially selected comb tooth geometry. An initial tooth overlap dimension is selected as a starting point. Using a computer aided design (CAD) program, a finite element model is constructed of at least one tooth pitch of the proposed tooth geometry. A finite element analysis calculation of capacitance is performed for both the selected initial tooth overlap dimension and for each of a plurality of different tooth overlap dimensions both greater than and less than the initial tooth overlap dimension. A polynomial fit of at least 4th order is performed for capacitance versus tooth overlap. The 3rd derivative of this polynomial is formed. The tooth overlap dimension that forces this 3rd derivative to zero is then determined. This amount of tooth overlap results in zero vibration rectification. According to another aspect of the invention, the desired amount of overlap is obtained through an empirical rather than analytical method. A number of test accelerometer devices are fabricated with varying tooth overlap dimensions, and vibration rectification measurements are made. When the range of fabricated geometries span the desired inflection point, interpolation of the test results yields the precise position of zero-rectification. According to one aspect of the invention, an accelerometer device constructed in accordance with the earlier steps of the method is calibrated to remove rectification errors due to manufacturing variations. These variations include unintended variations that move the ideal inflection point where rectification error is minimum or zero, and geometry variations that introduce a rectification error due to non-symmetries in gas-damping. Two calibration methods are presented. Each method repositions the moveable teeth slightly relative to the fixed teeth, whereby the closed-loop null position is at the actual zero rectification position. Calibrating the accelerometer device is achieved by either bleeding a non-zero bias voltage into the capacitive pick-off circuit of the accelerometer, or by changing one of the two pickoff excitation voltages relative to the other, while vibrating the accelerometer along an input axis thereof. Calibration is complete when the position is found where the resulting measured rectification error is zero. If the nominal comb drive geometry is as determined by the analytical or empirical methods of this invention, then the amount of displacement needed to reposition the moveable teeth to the desired position within an individual accelerometer is very small. The foregoing aspects and many of the attendant advantages of this invention will become more readily appreciated as the same becomes better understood by reference to the following detailed description, when taken in conjunction with the accompanying drawings, wherein: In the Figures, like numerals indicate like elements. The Figures illustrate the method of the present invention for determining a lateral comb drive geometry which minimizes or completely eliminates rectification and, at the same time, provides a sufficiently large force for a given drive area and applied voltage. The example shown in In Block In Block In Block Thus, the graph where dC/dx is the derivative of capacitance with respect to the overlap distance As is observed in the graph In Block In Block Analysis of the exemplary tooth geometry illustrated in According to this alternative embodiment of the method of the present invention, the tooth length In Block In Block In Block In Block Even with a comb-drive geometry selected per the method of the present invention, natural variation of the manufactured geometry causes a small, non-zero 2nd order electrostatic force-position derivative and, therefore, a rectification error. Manufacturing tolerances also result in slight non-symmetry in damping gap geometry, as discussed below. Therefore, even in the best example of a good design, two sources of small amounts of rectification are present. A net residual rectification is the sum of these two sources of rectification. According to the present invention, the net residual rectification is removed by commanding the proof mass Rectification due to gas-spring effects alone are potentially very large in MEMS accelerometers and other MEMS devices and therefore must be managed to achieve good performance. Therefore, according to one or more different embodiments of the present invention, this gas-spring effects source of rectification is optionally eliminated simultaneously with the rectification source resulting from the manufactured geometry by commanding the proof mass As discussed above, it is well known in the art of electrostatic accelerometers that the force between the two capacitor plates embodied by the movable and fixed comb drive teeth Furthermore, when the net residual rectification error is small enough at the initial null setting of the servo, cancellation alone works well over a narrow range in put amplitudes and frequency. While the preferred embodiment of the invention has been illustrated and described, it will be appreciated that various changes can be made therein without departing from the spirit and scope of the invention. Patent Citations
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